Bifurcation solutions and stability of a predator-prey model with fear effect. (Chinese. English summary) Zbl 1413.35065

Wang, Rong; Yang, Wenbin; Li, Yanling

Basic Sci. J. Text. Univ. 31, No. 1, 45-54 (2018).

Summary: The coexistence of the predator-prey model with fear effect is considered. By the method of spectral analysis and bifurcation theory, the bifurcation at the steady-state solutions is acquired by treating \(m\) as bifurcation parameters. Some stability results of the bifurcation solutions are obtained by using perturbation theory of linear operators and stability theory of bifurcation solutions. The results show that this system arises bifurcation phenomenon at the steady-state solution, and this bifurcation solution is unconditionally stable.

MSC:

35B32	Bifurcations in context of PDEs
35B35	Stability in context of PDEs
92D25	Population dynamics (general)

Keywords:

fear effect; predator-prey model; spectral analysis; stability; bifurcation theory